In a conventional digital data transmission system, a sequence of data bits is transmitted over a communications medium. A receiver then attempts to recreate the transmitted sequence. That is, for each received bit, the receiver determines whether the transmitted bit is more likely to have been a “1” or a “0”. In doing so, the receiver must deal with the fact that the received signal will not be a perfect copy of the transmitted bit sequence, but will show the effects of changes to the waveform introduced by the communications medium, and will include an additional noise component.
For many communications media, one source of changes to the waveform is inter-symbol-interference (ISI). That is, energy from one bit period is received in another bit period. In the case of optical fibres, ISI results from the fact that components of optical signals travel along an optical fibre at different speeds.
The presence of ISI greatly increases the probability that the receiver will fail to determine correctly whether a specific transmitted bit was a “1” or a “0”. That is, it greatly increases the probability of bit errors.
It is known, however, that it is possible to compensate for ISI to some extent. A particular transmitted waveform results in a particular received waveform, and the relationship between the transmitted waveform and the received waveform can be expressed mathematically as a transfer function. An equalizer can be provided in the receiver, which applies a second transfer function to the received waveform. If the second transfer function can be made to approximate the inverse of the first transfer function, then the effects of ISI can be approximately compensated.
Equalizers are known in which the equalizer output is compared with a target waveform, and the equalizer transfer function is automatically adapted using the well-known LMS algorithm, so that the equalizer output becomes closer to the target waveform.
It is also known that the signals can be represented by “eye diagrams”, which provide a way of showing the shapes of waveforms. Specifically, an eye diagram shows the shape of the waveform, during the course of a large number of bit periods, with the waveform shapes during the different bit periods being superimposed on each other. The waveform shape of a “1” in the signal should be very clearly different from the waveform shape of a “0” in the signal, leading to an open eye. However, in a distorted signal, the eye will appear more closed. The degree of eye opening therefore indicates the amount of distortion, although judgements about the degree of eye opening are generally qualitative rather than quantitative.